Lets solve our radical equation
step by step.
Step 1 add 4 to both sides of the equation:


Step 2 square both sides of the equation:



Step 3 expand the binomial in the right hand side:

Step 4 simplify the expression:


Step 5 factor the expression:

Step 6 solve for each factor:
or 
or 
Now we are going to check both solutions in the original equation to prove if they are valid:
For 


The solution
is a valid solution of the rational equation
.
For 



Since -3 is not equal to -5, the solution
is not a valid solution of the rational equation
; therefore,
is an extraneous solution of the equation.
We can conclude that even all the algebraic procedures of Israel are correct, he did not check for extraneous solutions.
An extraneous solution of an equation is the solution that emerges from the algebraic process of solving the equation but is not a valid solution of the equation. Is worth pointing out that extraneous solutions are particularly frequent in rational equation.
Answer:
324 square meters
Step-by-step explanation:
Hey there!
The surface area of a shape is the area of all the surfaces added up
The side surface area is 48 since 16 x 3 is 48. Since there are two side areas, we need to multiply 48 x 2 is 96
Now we need to do this for the other sides
the bottom and top areas are 96 square meters each so we multiply 96 by 2 which is 192
The front and back faces have an area of 18 square meters so we multiply 18 by 2 since there are two faces which are 36
Now we add all the values: 96+192+36 which is 324
So the surface area of the prism is 324 square meters
By definition of tangent,
tan(<em>x</em>) = sin(<em>x</em>) / cos(<em>x</em>)
so if tan(<em>x</em>) < 0, and we're given cos(<em>x</em>) = -1/4 < 0, then it follows that sin(<em>x</em>) > 0.
Recall the Pythagorean identity:
cos²(<em>x</em>) + sin²(<em>x</em>) = 1 → sin(<em>x</em>) = + √(1 - cos²(<em>x</em>))
Then
sin(<em>x</em>) = √(1 - (-1/4)²) = √(15/16) = √(15)/4
Recall the double angle identity:
sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)
Then
sin(2<em>x</em>) = 2 • √(15)/4 • (-1/4) = -2√(15)/16 = -√(15)/8
Answer:
x=0
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.